What is the integral of x^{3/2}+x^{7/4}+x^{2/3} ?

The integral of x^{3/2}+x^{7/4}+x^{2/3} is 2/5 x^{5/2}+4/11 x^{11/4}+3/5 x^{5/3}+C

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integral of x^{3/2}+x^{7/4}+x^{2/3}

\int x^{\frac{3}{2}} + x^{\frac{7}{4}} + x^{\frac{2}{3}} d x

\frac{2}{5} x^{\frac{5}{2}} + \frac{4}{11} x^{\frac{11}{4}} + \frac{3}{5} x^{\frac{5}{3}} + C

Solution steps

\int x^{\frac{3}{2}} + x^{\frac{7}{4}} + x^{\frac{2}{3}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{\frac{3}{2}} d x + \int x^{\frac{7}{4}} d x + \int x^{\frac{2}{3}} d x

\int x^{\frac{3}{2}} d x = \frac{2}{5} x^{\frac{5}{2}}

\int x^{\frac{7}{4}} d x = \frac{4}{11} x^{\frac{11}{4}}

\int x^{\frac{2}{3}} d x = \frac{3}{5} x^{\frac{5}{3}}

= \frac{2}{5} x^{\frac{5}{2}} + \frac{4}{11} x^{\frac{11}{4}} + \frac{3}{5} x^{\frac{5}{3}}

Add a constant to the solution

= \frac{2}{5} x^{\frac{5}{2}} + \frac{4}{11} x^{\frac{11}{4}} + \frac{3}{5} x^{\frac{5}{3}} + C

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What is the integral of x^{3/2}+x^{7/4}+x^{2/3} ?
The integral of x^{3/2}+x^{7/4}+x^{2/3} is 2/5 x^{5/2}+4/11 x^{11/4}+3/5 x^{5/3}+C